以下为句子列表：
英文: Firstly, the duality principle is used to change the linear program problem into the minimax problem, an interval extension of the adjustable entropy function is set up and its order of convergence is discussed.
中文: 首先利用对偶理论将线性规划问题转化为极大极小问题，建立并讨论了调节熵函数的区间扩张及其收敛阶。
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英文: In addition, theoretical studies associated with instrumental voting, e.g., the expected utility maximization model, the minimax regret model, and game-theoretic models cannot successfully explain the resulting voter turnouts.
中文: 投票工具论的相关模型，例如预期效用极大，极小极大后悔，以及赛局理论等模型，也未能成功地解释由实验所产生的投票率。
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英文: In the present paper, some theorems for variational inequalities and minimax inequality are obtained in hyperconvex metric spaces.
中文: 摘要文章给出了超凸度量空间中的一些变分不等式定理和极大极小不等式定理。
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英文: Some solvability conditions of periodic solutions are obtained for a class of first order superquadratic non-autonomous Hamiltonian systems in light of the minimax methods of critical point theory.
中文: 摘要运用临界点理论中的极小、极大方法得到一类超二次哈密顿系统的周期解的存在性的存在性定理。
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